Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
n = int(input())
m = 1
arr = []
while(True):
	mm = (m*(m+1))//2
	if mm>n:
		break
	arr.append(mm)
	m+=1

ll = len(arr)
flag = 0
for i in range(ll):
	curr = arr[i]
	req = n-curr
	l = i
	r = ll-1
	while(l<=r):
		mid = (l+r)//2
		if arr[mid]>=req:
			r = mid-1
		else:
			l = mid+1
	if i<=l<ll and arr[l]==req:
		flag=1
		break
if flag==1:
	print("YES")
else:
	print("NO")